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Physical Review A

Degenerate two-level system in the presence of a transverse magnetic field

L. Margalit, M. Rosenbluh, A. D. Wilson‐Gordon

Published Mar 12, 2013• 44 citations
Publisher

Abstract

The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the ${D}_{2}$ line of ${}^{87}$Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a $\ensuremath{\sigma}$ polarized pump in the Hanle configuration with that of a ${\ensuremath{\sigma}}^{\ensuremath{-}}$ probe in the presence of a ${\ensuremath{\sigma}}^{+}$ pump in the pump-probe configuration, and we show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to its magnitude. The population redistribution in the ground state due to the TMF is reinforced by collisional effects, leading to increased splitting of the coherent population trapping (CPT) dip in the absorption spectrum. We explain the appearance of the splitting by setting the quantization axis along the total magnetic field. Then, in the Hanle configuration, the direction of the quantization axis changes as the longitudinal magnetic field is scanned, so that the laser polarization also changes. This leads to the creation of new two-photon detuned $\ensuremath{\Lambda}$ subsystems. The evolution of the populations and coherences of the ground-state Zeeman sublevels is illustrated using the angular momentum probability surface. In addition to being split, the CPT dip in the pump-probe configuration is also shifted by the longitudinal magnetic field, so that the effects of the longitudinal and transverse magnetic fields can be distinguished from each other.

DOI
10.1103/physreva.87.033808

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We discuss the effect of static and time-dependent longitudinal and transverse magnetic fields on degenerate two-level and three-level systems in Rb atomic vapor. The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the D2 line of 87Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a σ polarized pump in the Hanle configuration with that of a σ− probe in the presence of a σ+ pump in the pump-probe configuration, and show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to the magnitude of the TMF. Coherent population trapping (CPT) transients induced by a modulated longitudinal magnetic field (LMF) are investigated theoretically for a realistic three-level Λ system in the D1 line of 87Rb. The contributions to the transient probe absorption from the various subsystems that comprise the realistic atomic system are examined and the absorption of each Λ subsystem is compared to that of a simple Λ system. We also present theoretical results for CPT transients induced by a modulated TMF. The application of a TMF leads to the appearance of new Λ subsystems, the creation of new dark states and the rearrangement of the population among the Zeeman sublevels. We show that transients appear as the system is switched between various steady-state situations and we identify the various components of the total probe absorption.

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We investigate the absorption spectra for the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=0$ transition of the ${D}_{2}$ line of $^{87}\mathrm{Rb}$ excited by a linearly polarized light in the presence of a transverse magnetic field (TMF) in different directions. Using the theoretical methods in quantum optics, we obtain the analytical expressions for the atomic density-matrix elements and the absorption spectrum. We analyze the splitting proportional to the magnitude of the TMF in the coherent population trapping absorption spectrum and explain its physical origin. Then, the sensitivity of the resonance signal to the phase (in our case, to the angle between the TMF and the light polarization) is investigated. We show and explain the splitting of the bright resonance and find the simple dependence of the separation of this splitting on the magnitude and the direction of the TMF. Therefore, this system may provide a possible method for the measurement of the magnetic field vector. In addition, we study the coherence of the system based on an observable coherence measure, namely, robustness of coherence (ROC). We find that in the case where the absorption signal becomes difficult to detect, the change of the ROC spectrum becomes more obvious and the extreme points are well maintained. Therefore, this may provide a scheme for the measurement of the magnetic field which is complementary to that based on the absorption signal of the laser.

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Transverse magnetic field effect on the giant Goos–Hänchen shifts based on a degenerate two-level system

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Abstract We study the effect of the Goos–Hänchen (GH) shifts through a cavity with degenerate two-level systems in the line of . For this purpose, we focus on the transverse magnetic field (TMF) in a Floquet frame to obtain the giant GH shifts. Physically, the collisional effects of TMF lead to increasing the population trapping in the ground state. However, we demonstrate that the population trapping generates the large negative or positive GH shifts and simultaneously switches from superluminal to subluminal (or vice versa). Also, we investigate the other optical properties such as the longitudinal magnetic field (LMF), which plays an important role in the control of the GH shifts and leads to the generation of new subsystems. In the next step, we evaluate the GH shifts beyond the multi-photon resonance condition by the control of TMF. Moreover, we compute the appearance of negative and positive GH shifts by setting the width of the incident Gaussian beams in the presence of a multi-photon resonance condition. Our results show that superluminal or subluminal light propagation can be simultaneously controlled by adjusting the rates of the TMF and LMF. The significant effects of these factors on the degenerate two-level systems provide different applications such as slow light, optical switches and quantum information storage.

Laser Physics Letters•Apr 26, 2018•3 citations
The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the D2{D}_{2}D2​ line of 87{}^{87}87Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a \ensuremathσ\ensuremath{\sigma}\ensuremathσ polarized pump in the Hanle configuration with that of a \ensuremathσ\ensuremath−{\ensuremath{\sigma}}^{\ensuremath{-}}\ensuremathσ\ensuremath− probe in the presence of a \ensuremathσ+{\ensuremath{\sigma}}^{+}\ensuremathσ+ pump in the pump-probe configuration, and we show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to its magnitude. The population redistribution in the ground state due to the TMF is reinforced by collisional effects, leading to increased splitting of the coherent population trapping (CPT) dip in the absorption spectrum. We explain the appearance of the splitting by setting the quantization axis along the total magnetic field. Then, in the Hanle configuration, the direction of the quantization axis changes as the longitudinal magnetic field is scanned, so that the laser polarization also changes. This leads to the creation of new two-photon detuned \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ subsystems. The evolution of the populations and coherences of the ground-state Zeeman sublevels is illustrated using the angular momentum probability surface. In addition to being split, the CPT dip in the pump-probe configuration is also shifted by the longitudinal magnetic field, so that the effects of the longitudinal and transverse magnetic fields can be distinguished from each other.
We discuss the effect of static and time-dependent longitudinal and transverse magnetic fields on degenerate two-level and three-level systems in Rb atomic vapor. The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the D2 line of 87Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a σ polarized pump in the Hanle configuration with that of a σ− probe in the presence of a σ+ pump in the pump-probe configuration, and show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to the magnitude of the TMF. Coherent population trapping (CPT) transients induced by a modulated longitudinal magnetic field (LMF) are investigated theoretically for a realistic three-level Λ system in the D1 line of 87Rb. The contributions to the transient probe absorption from the various subsystems that comprise the realistic atomic system are examined and the absorption of each Λ subsystem is compared to that of a simple Λ system. We also present theoretical results for CPT transients induced by a modulated TMF. The application of a TMF leads to the appearance of new Λ subsystems, the creation of new dark states and the rearrangement of the population among the Zeeman sublevels. We show that transients appear as the system is switched between various steady-state situations and we identify the various components of the total probe absorption.
We computationally compare Hanle-type resonances for a transition of the line for magnetic field scans parallel (longitudinal scan) and perpendicular (transverse scan) to the direction of propagation of the optical field in the presence of an additional transverse magnetic field (TMF). For a linearly polarized light, the coherent population trapping (CPT) resonances split at line centre and are identical for both longitudinal and transverse scans. When the probe beam ellipticity is varied, the effect of the TMF is found to be opposite for longitudinal and transverse scans. For a longitudinal scan, the splitting observed in the CPT resonance evolves into an enhanced absorption resonance with an increase in ellipticity. For a transverse scan, the splitting vanishes at higher ellipticities. This can be understood in terms of population redistribution in the ground state sublevels and near-neighbor ground state coherences created by the TMF. We also show that the enhanced absorption signal that splits the CPT resonance strongly depends on transit time, and the CPT resonance strength depends on the excited state dephasing rate.
We investigate the absorption spectra for the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=0$ transition of the D2{D}_{2}D2​ line of 87Rb^{87}\mathrm{Rb}87Rb excited by a linearly polarized light in the presence of a transverse magnetic field (TMF) in different directions. Using the theoretical methods in quantum optics, we obtain the analytical expressions for the atomic density-matrix elements and the absorption spectrum. We analyze the splitting proportional to the magnitude of the TMF in the coherent population trapping absorption spectrum and explain its physical origin. Then, the sensitivity of the resonance signal to the phase (in our case, to the angle between the TMF and the light polarization) is investigated. We show and explain the splitting of the bright resonance and find the simple dependence of the separation of this splitting on the magnitude and the direction of the TMF. Therefore, this system may provide a possible method for the measurement of the magnetic field vector. In addition, we study the coherence of the system based on an observable coherence measure, namely, robustness of coherence (ROC). We find that in the case where the absorption signal becomes difficult to detect, the change of the ROC spectrum becomes more obvious and the extreme points are well maintained. Therefore, this may provide a scheme for the measurement of the magnetic field which is complementary to that based on the absorption signal of the laser.
We experimentally and computationally study the effect of an additional transverse magnetic field (TMF) on the Hanle resonance for a F g = 2 → F e = 3 transition of 87Rb D 2 line for magnetic field scans perpendicular to the propagation direction of the optical field. It is shown that with a π-polarized light, no resonance signal is observed in absence of the TMF. When the TMF is applied, two peaks are observed on either side of zero scanning magnetic field in the transmission spectrum. The separation between the two peaks is linearly proportional to magnitude of the TMF, which can be used for magnetometry. We applied this technique to measure magnetic field from 0.1 to 0.5 G with a pure Rb vapor cell and from 10 to 30 mG with a Rb cell containing buffer gas. These observations are attributed to the population redistribution among the ground state sublevels due to the TMF.
We present theoretical results of coherent-population-trapping transients induced by a modulated transverse magnetic field (TMF). The application of a transverse magnetic field causes the appearance of new $\ensuremath{\Lambda}$ subsystems, creation of new dark states, and rearrangement of the population among the Zeeman sublevels. We show that transients appear as the system is switched between steady-state situations, and we identify the various level system components of the total probe absorption. We discuss the time-dependent evolution of the probe absorption caused by the modulated TMF in the presence and absence of a constant longitudinal magnetic field (LMF). The differences between TMF modulation and LMF modulation are discussed.
Abstract We study the effect of the Goos–Hänchen (GH) shifts through a cavity with degenerate two-level systems in the line of . For this purpose, we focus on the transverse magnetic field (TMF) in a Floquet frame to obtain the giant GH shifts. Physically, the collisional effects of TMF lead to increasing the population trapping in the ground state. However, we demonstrate that the population trapping generates the large negative or positive GH shifts and simultaneously switches from superluminal to subluminal (or vice versa). Also, we investigate the other optical properties such as the longitudinal magnetic field (LMF), which plays an important role in the control of the GH shifts and leads to the generation of new subsystems. In the next step, we evaluate the GH shifts beyond the multi-photon resonance condition by the control of TMF. Moreover, we compute the appearance of negative and positive GH shifts by setting the width of the incident Gaussian beams in the presence of a multi-photon resonance condition. Our results show that superluminal or subluminal light propagation can be simultaneously controlled by adjusting the rates of the TMF and LMF. The significant effects of these factors on the degenerate two-level systems provide different applications such as slow light, optical switches and quantum information storage.